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Mirrors > Home > ILE Home > Th. List > nfs1v | GIF version |
Description: 𝑥 is not free in [𝑦 / 𝑥]𝜑 when 𝑥 and 𝑦 are distinct. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfs1v | ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbs1 1950 | . 2 ⊢ ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑) | |
2 | 1 | nfi 1473 | 1 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1471 [wsb 1773 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 |
This theorem is referenced by: nfsbxy 1954 nfsbxyt 1955 sbco3v 1981 sbcomxyyz 1984 sbnf2 1993 mo2n 2066 mo23 2079 mor 2080 clelab 2315 cbvralf 2714 cbvrexf 2715 cbvralsv 2738 cbvrexsv 2739 cbvrab 2754 sbhypf 2805 mob2 2936 reu2 2944 sbcralt 3058 sbcrext 3059 sbcralg 3060 sbcreug 3062 sbcel12g 3091 sbceqg 3092 cbvreucsf 3141 cbvrabcsf 3142 disjiun 4020 cbvopab1 4098 cbvopab1s 4100 csbopabg 4103 cbvmptf 4119 cbvmpt 4120 opelopabsb 4285 frind 4377 tfis 4607 findes 4627 opeliunxp 4706 ralxpf 4798 rexxpf 4799 cbviota 5208 csbiotag 5235 isarep1 5328 cbvriota 5872 csbriotag 5874 abrexex2g 6160 abrexex2 6164 dfoprab4f 6233 finexdc 6945 ssfirab 6977 uzind4s 9641 zsupcllemstep 12056 bezoutlemmain 12109 nnwosdc 12150 cbvrald 15204 bj-bdfindes 15365 bj-findes 15397 |
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